Frequency-Comb Spectrum of Periodic-Patterned Signals

Using arbitrary periodic pulse patterns we show the enhancement of specific frequencies in a frequency comb. The envelope of a regular frequency comb originates from equally spaced, identical pulses and mimics the single pulse spectrum. We investigated spectra originating from the periodic emission of pulse trains with gaps and individual pulse heights, which are commonly observed, for example, at high-repetition-rate free electron lasers, high power lasers, and synchrotrons. The ANKA synchrotron light source was filled with defined patterns of short electron bunches generating coherent synchrotron radiation in the terahertz range. We resolved the intensities of the frequency comb around 0.258 THz using the heterodyne mixing spectroscopy with a resolution of down to 1 Hz and provide a comprehensive theoretical description. Adjusting the electron’s revolution frequency, a gapless spectrum can be recorded, improving the resolution by up to 7 and 5 orders of magnitude compared to FTIR and recent heterodyne measurements, respectively. The results imply avenues to optimize and increase the signal-to-noise ratio of specific frequencies in the emitted synchrotron radiation spectrum to enable novel ultrahigh resolution spectroscopy and metrology applications from the terahertz to the x-ray region.

Figure 1

Scheme of a signal pattern $s_0$ which repeats after the period time $T_0=1/f_0=h{T}_p$. $T_p$ denotes the time between consecutive pulses with individual height and $h$ the number of slots. Here, the signal consists of a train of 5 pulses and a gap of 3 slots.

Figure 2

${|\mathrm{DFT}|}^2$ of five consecutive pulses with distance ${\mathrm{T}}_p$. According to Eq. (6), the DFT is sampled at discrete multiples of $f_0=f_P/h$. Two exemplary cases are shown: Without a gap ($h=5$) the DFT is sampled at multiples of $f_0=f_P/5$ (green crosses). If a gap of three slots is added ($h=8$) it is sampled at multiples of $f_0=f_P/8$ (red dots). Solid line: all five pulses have the same height; dotted line: filling pattern as in Fig 1. Note how the uneven filling pattern leads to a sizable contribution at the zeros of the even filling pattern.

Figure 3

Measured synchrotron radiation shows discrete harmonics of the revolution frequency at 259 GHz. The aliased LSB is shown in grey. For data reduction, only the intensity of each harmonic is used in the following, as shown on the right.

Figure 4

Measured THz power spectrum at discrete multiples of the revolution frequency $f_0$ for different filling patterns. The right panel shows the corresponding filling pattern. The blue line corresponds to the initial filling pattern of 4 trains with 33 bunches each. For the red data set every second bunch was removed and for the green line only every fourth bunch is kept. For the purple line, only a single bunch is left leading to a 2.71 MHz frequency comb with almost equal power at all observed frequency teeth, differing only by 2 dB. For better visibility the red and blue data sets were shifted by $+5\mathrm{dB}$ and $+10\mathrm{dB}$, respectively. The displayed average noise level was $-100\mathrm{dBm}$.